Problem: Solve for $x$ and $y$ using elimination. ${6x+2y = 52}$ ${5x-2y = 25}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $11x = 77$ $\dfrac{11x}{{11}} = \dfrac{77}{{11}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {6x+2y = 52}\thinspace$ to find $y$ ${6}{(7)}{ + 2y = 52}$ $42+2y = 52$ $42{-42} + 2y = 52{-42}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 7}$ into $\thinspace {5x-2y = 25}\thinspace$ and get the same answer for $y$ : ${5}{(7)}{ - 2y = 25}$ ${y = 5}$